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Popular >

((ln(x))/(x^2))^'

Solution

(\frac{ln ( x )}{x ^{2}})^{^{'}}

Solution

\frac{1 - 2 ln ( x )}{x ^{3}}

Solution steps

(\frac{ln ( x )}{x ^{2}})^{'}

Apply the Quotient Rule:

(\frac{f}{g})^{'} = \frac{f ^{'} \cdot g - g ^{'} \cdot f}{g ^{2}}

= \frac{( ln ( x ) ) ^{^{'}} x ^{2} - ( x ^{2} ) ^{^{'}} ln ( x )}{( x ^{2} ) ^{2}}

(ln (x))^{'} = \frac{1}{x}

(x^{2})^{'} = 2 x

= \frac{\frac{1}{x} x ^{2} - 2 x ln ( x )}{( x ^{2} ) ^{2}}

Simplify

\frac{\frac{1}{x} x ^{2} - 2 x ln ( x )}{( x ^{2} ) ^{2}} : \frac{1 - 2 ln ( x )}{x ^{3}}

= \frac{1 - 2 ln ( x )}{x ^{3}}

Popular Examples

(\partial)/(\partial x)(cos^7(x^9y^5))

\frac{\partial}{\partial x} (cos^{7} (x^{9} y^{5}))

derivative of y=(4-xe^x)/(x+e^x)derivative of

y = \frac{4 - x e ^{x}}{x + e ^{x}}

integral of x^2 1/x

\int x^{2} \frac{1}{x} d x

integral from 4 to 7 of 1/(x^2-1)

\int_{4}^{7} \frac{1}{x ^{2} - 1} d x

\frac{d y}{d x} = 6 x + 2

Frequently Asked Questions (FAQ)

What is the ((ln(x))/(x^2))^' ?
The ((ln(x))/(x^2))^' is (1-2ln(x))/(x^3)
What is the first ((ln(x))/(x^2))^' ?
The first ((ln(x))/(x^2))^' is (1-2ln(x))/(x^3)